TitleTowards a theory of quantum integrability in finite size systems
NameOwusu, Haile (author), Yuzbashyan, Emil (chair), Wu, Weida (internal member), Baker, Andrew (internal member), Andrei, Natan (internal member), Rutgers University, Graduate School - New Brunswick,
SubjectPhysics and Astronomy,
Quantum field theory
DescriptionWe study general quantum integrable Hamiltonians linear in a coupling constant and represented by finite NxN real symmetric matrices. The restriction on the coupling dependence leads to a natural notion of nontrivial integrals of motion and classification of integrable families into Types according to the number of such integrals. A Type M family in our definition is formed by N-M nontrivial mutually commuting operators linear in the coupling. Working from this definition alone, we parameterize Type M operators, i.e. resolve the commutation relations, and obtain an exact solution for their eigenvalues and eigenvectors. We show that our parameterization covers all Type 1, 2, and 3 integrable models and discuss the extent to which it is complete for other types. We also present robust numerical observation on the number of energy level crossings in Type M integrable systems and analyze the taxonomy of types in the 1d Hubbard model.
NoteIncludes bibliographical references
Noteby Haile Owusu
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.